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Bjorner and Ekedahl (Ann. of math., 2008) proved that lower Bruhat intervals of crystallographic Coxeter groups are top-heavy using Hodge theory. Using Soergel bimodules and their Hodge theory establi...
The unimodality of lower Bruhat intervals for the “upper half” remains as an open problem. For affine Weyl group W with corresponding finite Weyl group W_f, we prove that lower W_f-parabolic Bruhat in...
Thus far, likelihood-based interval estimates for quantiles have not been studied in the literature on interval censored case 2 data and partly interval censored data, and, in this context, the use of...
Monte Carlo methods are used to approximate the means, μ, of random variables Y, whose distributions are not known explicitly. The key idea is that the average of a random sample, Y1,...,Yn, tends t...
We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial i...
For a minimal diffusion process on $ (a,b) $, any possible extension of it to a standard process on $ [a,b] $ is characterized by the characteristic measures of excursions away from the boundary point...
It is proved that the average length of standard confidence intervals for parameters of gamma and normal distributions monotonically decrease with the sample size. The proofs are based on fine propert...
Abstract: In \cite{BCKM} it was shown that "Tiling implies Spectral" holds for a union of three intervals and the reverse implication was studied under certain restrictive hypotheses on the associated...
Abstract: We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [T, T'] where T and T' are balanced binary trees are isomorphic as ...
Abstract: This book has eleven chapters. Chapter one describes all types of natural class of intervals and the arithmetic operations on them. Chapter two introduces the semigroup of natural class of i...
The cascade model generates a food web at random. In it the species are labeled from 0 to $m$, and arcs are given at random between pairs of the species. For an arc with endpoints $i$ and $j$ ($i
We consider the Gel’fand inverse problem and continue studies of [Mandache,2001].We show that the Mandache-type instability remains valid even in the case of Dirichletto-Neumann map given on the energ...
We consider random multiplicative functions taking the values $\pm 1$. Using Stein's method for normal approximation, we prove a central limit theorem for the sum of such multiplicative functions in a...
Assume the Riemann Hypothesis. For every ǫ > 0 we show that there is a constant C(ǫ) such that for all large x, the interval [x, x + C(ǫ)px] contains an integer all of whose prime facto...
A Sabidussi graph is defined from a total order T and a graph G as follows. Choose a vertex of G and denote it by 0. Denote by V(T)V(G) the family of the functions f :V(T)¡!V(G) such that fq 2...

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